Roboguru

Sederhanakanlah bentuk-bentuk pangkat berikut.

Pertanyaan

Sederhanakanlah bentuk-bentuk pangkat berikut.

begin mathsize 14px style 5 open parentheses a b squared c cubed close parentheses to the power of negative 3 end exponent cross times 2 squared a b squared divided by 10 a to the power of 7 c to the power of negative 1 end exponent equals space... space end style 

Pembahasan Soal:

Gunakan sifat bentuk eksponen berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses a b close parentheses to the power of n end cell equals cell a to the power of n times b to the power of n end cell row cell a to the power of m times a to the power of n end cell equals cell a to the power of m plus n end exponent end cell row cell a to the power of m over a to the power of n end cell equals cell a to the power of m minus n end exponent end cell row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m cross times n end exponent end cell row cell a to the power of negative n end exponent end cell equals cell 1 over a to the power of n end cell end table end style  

Perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell 5 left parenthesis a b squared c cubed right parenthesis to the power of negative 3 end exponent cross times 2 to the power of 2 end exponent a b squared divided by 10 a to the power of 7 c to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 5 left parenthesis a b squared c cubed right parenthesis to the power of negative 3 end exponent cross times 2 to the power of 2 end exponent a b squared over denominator 10 a to the power of 7 c to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 5 a to the power of 1 cross times open parentheses negative 3 close parentheses end exponent b to the power of 2 cross times open parentheses negative 3 close parentheses end exponent c to the power of 3 cross times open parentheses negative 3 close parentheses end exponent cross times 4 a b squared over denominator 10 a to the power of 7 c to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 20 a to the power of negative 3 end exponent b to the power of negative 6 end exponent c to the power of negative 9 end exponent cross times a b squared over denominator 10 a to the power of 7 c to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 20 a to the power of negative 3 plus 1 end exponent b to the power of negative 6 plus 2 end exponent c to the power of negative 9 end exponent over denominator 10 a to the power of 7 c to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 20 a to the power of negative 2 end exponent b to the power of negative 4 end exponent c to the power of negative 9 end exponent over denominator 10 a to the power of 7 c to the power of negative 1 end exponent end fraction end cell row blank equals cell 2 a to the power of negative 2 minus 7 end exponent b to the power of negative 4 end exponent c to the power of negative 9 minus open parentheses negative 1 close parentheses end exponent end cell row blank equals cell 2 a to the power of negative 9 end exponent b to the power of negative 4 end exponent c to the power of negative 8 end exponent end cell row blank equals cell fraction numerator 2 over denominator a to the power of 9 b to the power of 4 c to the power of 8 end fraction end cell end table end style 

Jadi, bentuk sederhanya adalah begin mathsize 14px style fraction numerator 2 over denominator a to the power of 9 b to the power of 4 c to the power of 8 end fraction end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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